From lignin to spruce: Poromechanical upscaling of wood strength
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From lignin to spruce: Poromechanical upscaling of wood strength Thomas K. Bader1, K. Hofstetter1, Ch. Hellmich1, Josef Eberhardsteiner1 1 Institute for Mechanics of Materials and Structures, Vienna University of Technology, A-1040 Vienna, Austria ABSTRACT Wood strength is highly anisotropic, due to the inherent structural hierarchy of the material. In the framework of a combined random-periodic multiscale poro-micromechanics model, we here translate compositional information throughout this hierarchy into the resulting anisotropic strength at the softwood level, based on “universal” elastic properties of cellulose, hemicelluloses, and lignin, and on the shear strength of the latter elementary constituent. Therefore, derivation of the elastic energy in a piece (representative volume element – RVE) of softwood, stemming from homogeneous macroscopic strains prescribed in terms of displacements at the boundary of the RVE and from pressure exerted by water filling the nanoporous space between the hemicelluloses-lignin network within the cell walls, with respect to the shear stiffness of lignin, yields higher order strains in the lignin phase, approximating micro-stress peaks leading to local lignin failure. Relating this (quasi-brittle) failure to overall softwood failure (or strictly speaking, elastic limit of softwood) results in a macroscopic microstructure-dependent failure criterion for softwood. The latter satisfactorily predicts the biaxial strength of spruce at various loading angles with respect to the grain direction. The model also predicts the experimentally well-established fact that uniaxial tensile and compressive strengths, as well as the shear strength of wood, depend quasi-linearly on the cell water content, but highly nonlinearly on the lumen porosity. INTRODUCTION It is well accepted that changes in lumen porosity, as well as such in cell wall composition are the key factors governing wood strength magnitude and anisotropy. However, what remains a matter of discussion is how wood strength is functionally dependent on the aforementioned key factors. In this context, correlations between respective experimental data are often expressed in terms of empirical relations [1,6,13]. However, such relations are, as a rule, restricted in applicability and reliability, since they do not explicitly consider the mechanical behavior of the complex hierarchical microstructure of wood, which underlies the aforementioned correlations. As a remedy, we here aim at predicting relationships between porosity/composition and strength (i.e. brittle ultimate strength and yield limit in case of ductile behavior) in a micromechanical framework including random as well as periodic homogenization techniques [12,14]. THEORY AND EXPERIMENTAL VALIDATION By combining a recently developed poroelastic multiscale model for softwood [2,7] with a von Mises-type failure criterion for lignin, we derive a species and specimen-specific multiscale model for lignin-related elastic limits in softwood (see figure 1). This model rests on “univers
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